Pressure Measuring Devices

  

 DIFFERENTIAL MANOMETERS

# INTRODUCTION:

   Differential manometer is used to measure the difference of pressure between two points in pipe or two different pipes. There are two types of differential manometers.
1) U-tube upright differential manometer.
2) U-tube inverted differential manometer.

1)U-tube upright differential manometer

It is used to measure the difference in pressure between two pipes or two different level.
Case 1:   U-tube upright differential manometer connected at two points in a pipe at same level.
The construction and arrangement of a manometer connected at two different points, A and B, of a pipe is shown in figure 1.1.
        Fig. 1.1 U-tube upright differential                                    manometer
Let,         
ρ1 = density of liquid flowing in the pipeline
ρ2 = density of manometer liquid (assume mercury)
S = Specific gravity of liquid for which pressure has to be determined
S1 = Specific gravity of manometer liquid
hA be the pressure in terms of height of fluid in the pipe at point A
hB be the pressure in terms of height of fluid in the pipe at point B
h is the distance of mercury level in the right limb from the datum line XX
h1 is the height of manometer liquid level in the right limb from the centre of pipe at point B
Pressure difference at two points in a pipe
Left limb = hA+(h+h1)S...............(1)
Right limb = hB+h1S+hS1.............(2)
*Pressure is same at datum line:
hA+(h+h1)S = hB+h1+hS1
hA-hB = -h1S1-hS+-h1S+hS1


Case 2 - U-tube upright differential manometer connected between two pipes at different levels and carrying different fluids.
      Fig.1.2 Vertical differential manometer (pressure difference between two pipes)
Let,         
S1 = Specific gravity of liquid in pipe A
S2 = Specific gravity of liquid in pipe B
S = Specific gravity of manometer liquid
hA be the pressure head in terms of height of fluid in the pipe at point A
hB be the pressure head in terms of height of fluid in the pipe at point B
h is the distance of mercury level in the right limb from the datum line XX
h1 is the height of manometer liquid level in the left limb from the from the datum line XX
h2 is the height of manometer liquid level in the right limb from the from the centre of pipe at point B.

Leftlimb eq =  hA+h1S1.................(1)

Rightt limb eq = hB+h2S2+hS...........(2)

*Pressure is same at datum line:

hA+h1S1 = hB+h2S2+hS

hA-hB=h1S1-h2S2+hS 

2)U-tube Inverted Differential Manometer

In such types of manometers light fluids for e.g. oil is used as manometer fluid. In the previous derivation, the term  is added, but here in the left and right limb equations, it is necessary to subtract  term.

Fig. 1.3. Inverted differential manometel   Let                                                                
S1 = Specific gravity of liquid in pipe A.
S2 = Specific gravity of liquid in pipe B.
S = Specific gravity of manometer liquid.
hA be the pressure head in terms of height of fluid in the pipe at point A.
hB be the pressure head in terms of height of fluid in the pipe at point B.
h is the distance of manometer liquid level in the right limb from the datum line XX.
h1 is the height of manometer liquid level in the left limb from the from the datum line XX.
h2 is the height of manometer liquid level in the right limb from the from the centre of pipe at point B.

Left limb eq = hA –h1S1................................(1)
Rightt limb eq = hB-h2S2-hS...........(2)
*Pressure is same at datum line:
hA+h1S1=hB-h2S2-hS
hA-hB=h1S1-h2S2-hS

 #Numerical:       

1)  Two pipes on the same elevation convey water and oil of specific gravity 0.88 respectively. They are connected by a U-tube manometer with the manometric liquid having a specific gravity of 1.25. If the manometric liquid in the limb connecting the water pipe is 2 m higher than the other find the pressure difference in two pipes.

Solution:                                                      

             Given data:

                 Height difference = 2
m
                 Specific gravity of oil s = 0.88
                 Specific gravity of manometric liquid s = 1.25
                 Equating pressure head at section (A-A)
Formula                                                        
P1 +2×1.25×1000×9.81+(5-2)1000×9.81=p2+5×0.88×1000×9.81

               Substituting h = 5 m and density of water 998.2 kg/m3 we have P A -P B = 10791

              Answer:-  10791 Pa  

#For video refrencre:

   https://youtu.be/S9qIOnFcE9g


References:      P. N. Modi , cengel Boles Tata McGraw Hill              

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